On the direct insulatorquantum Hall transition in twodimensional electron systems in the vicinity of nanoscaled scatterers
 ChiTe Liang^{1}Email author,
 LiHung Lin^{2},
 Chen Kuang Yoa^{1},
 ShunTsung Lo^{1},
 YiTing Wang^{1},
 DongSheng Lou^{3},
 GilHo Kim^{4},
 Chang YuanHuei^{1},
 Yuichi Ochiai^{5},
 Nobuyuki Aoki^{5},
 JengChung Chen^{3},
 Yiping Lin^{3},
 Huang ChunFeng^{6},
 ShengDi Lin^{7} and
 David A Ritchie^{8}
DOI: 10.1186/1556276X6131
© Liang et al; licensee Springer. 2011
Received: 14 August 2010
Accepted: 11 February 2011
Published: 11 February 2011
Abstract
A direct insulatorquantum Hall (IQH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different twodimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct IQH transition, and the transport properties under different nanaoscaled scatterers are discussed.
Introduction
The simultaneous presence of disorder and a strong enough magnetic field B can lead to a wide variety of interesting physical phenomena. For example, the integer quantum Hall effect is one of the most exciting effects in twodimensional electron systems (2DES), in which the electrons are usually confined in layers of the nanoscale [1]. In an integer quantum Hall (QH) state, the current is carried by the onedimensional edge channels because of the localization effects. It has been shown that with sufficient amount of disorder, a 2DES can undergo a Binduced insulator to quantum Hall transition [2–5]. Experimental evidence for such an insulatorquantum Hall (IQH) transition is an approximately temperature (T)independent point in the measured longitudinal resistivity of a 2DES [3–5]. The IQH transition continues to attract a great deal of interest both experimentally and theoretically as it may shed light on the fate of extended states [6–10], the true ground state of a noninteracting 2DES [2], and a possible metalinsulator transition in 2D [11, 12].
It is worth pointing out that in order to observe an IQH transition separating the zerofield insulator from the QH liquid, one needs to deliberately introduce strong disorder within a 2DES. The reason for this is that the localization length needs to be shorter than the sample size. In the study by Jiang and coworkers [2], a 2DES without a spacer layer in which strong Coulomb scattering exists was used. Wang et al. utilized a 30nmthick heavily doped GaAs layer so as to allow the positively charged Si atoms to introduce longrange random potential in the 2DES [3]. Hughes et al. have shown that when a Sidoped plane was incorporated into a 550nmthick GaAs film, a deep potential well can form in which the 2DES is confined close to the ionized donors and is therefore highly disordered [4]. It has been shown that by deliberately introducing nanoscaled InAs quantum dots [13] in the vicinity of a modulationdoped GaAs/AlGaAs heterostructure, a strongly disordered 2DES which shows an IQH transition can be experimentally realized [14, 15].
The transition/crossover from an insulator to a QH state of the filling factor ν > 2 in an ideal spinless 2DES can be denoted as the direct IQH transition [16–19]. Such a transition has been attracting a great deal of interest and remains an unsettled issue. Experimental [16–19] and theoretical results [9, 10] suggest that such a direct transition can occur, and it is a quantum phase transition. However, Huckestein [20] has argued that such a direct transition is not a quantum phase transition, but a narrow crossover in B due to weak localization to Landau quantization.
In this study, the authors compare three different electron systems containing nanoscaled scatterers which all show a direct IQH transition. The first sample is a GaAs 2DES containing selfassembled nanoscaled InAs quantum dots [13, 14, 21–23].
The second one is a 2DES in a nominally undoped AlGaN/GaN heterostructure [24–33] grown on Si substrate [33, 34]. Such a GaNbased electron system can be affected by nanoscaled dislocation and impurities [35]. Finally, experimental results on the third sample, a deltadoped GaAs/AlGaAs quantum well with additional modulation doping [36, 37], will be presented. All the experimental results on the three completely different samples show that the direct IQH transition does not occur with the onset of strong localization due to Landau quantization [20, 38]. Therefore, in order to obtain a thorough understanding of the direct IQH transition, further studies are required.
Experimental details
Results and discussions
It has been suggested that by converting the measured resistivities into longitudinal and Hall conductivities, it is possible to shed more light on the observed IQH transition [5]. Figure 6 shows such results at various temperatures. Interestingly, for B < 5 T, _{σ} _{ xy } is nominally T independent. Such data are consistent with electronelectron interaction effects. Over the whole measurement range, σ_{ xx } decreases with increasing T, consistent with electronelectron interaction effects. Unlike σ_{ xy }, σ_{ xx } shows a significant T dependence.
Conclusions
In conclusion, the authors have presented studies on three completely different electron systems. In these three samples, the nanoscaled scatterers, in close proximity of the 2DES, provide necessary disorder for observing the direct IQH transition. In these studies, it has been shown that the crossover from localization to Landau quantization actually covers a wide range of magnetic field. Moreover, the observed direct IQH transition is not necessarily linked with Landau quantization as no resistance oscillations are observed even up to a magnetic field 4 T higher than the crossing field. Most importantly, the onset of strong localization which gives rise to the formation of quantum Hall state does not correspond to the direct IQH transition. All these three pieces of experimental evidence show that a 2DES in the vicinity of nanoscaled scatterers is an ideal playground for studying the direct IQH transition. Furthermore, in order to obtain a thorough understanding of the underlying physics of the direct IQH transition, modifications of Huckestein's model [20] must be made.
Abbreviations
 IQH:

insulatorquantum Hall
 SdH:

Shubnikovde Haas
 2DESs:

twodimensional electron systems.
Declarations
Acknowledgements
This research was supported by the WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. R322008000102040). C.T.L. acknowledges financial support from the NSC (Grant no: NSC 992119M002018MY3). The authors would like to thank YiChun Su and JauYang Wu for providing help in the experiments.
Authors’ Affiliations
References
 von Klitzing K, Dorda G, Pepper M: New Method for HighAccuracy Determination of the FineStructure Constant Based on Quantized Hall Resistance. Phys Rev Lett 1980, 45: 494. 10.1103/PhysRevLett.45.494View Article
 Kivelson S, Lee DH, Zhang SC: Global phase diagram in the quantum Hall effect. Phys Rev B 1992, 46: 2223. 10.1103/PhysRevB.46.2223View Article
 Jiang HW, Johnson CE, Wang KL, Hannah ST: Observation of magneticfieldinduced delocalization: Transition from Anderson insulator to quantum Hall conductor. Phys Rev Lett 1993, 71: 1439. 10.1103/PhysRevLett.71.1439View Article
 Wang T, Clark KP, Spencer GF, Mack AM, Kirk WP: Magneticfieldinduced metalinsulator transition in two dimensions. Phys Rev Lett 1994, 72: 709. 10.1103/PhysRevLett.72.709View Article
 Hughes RJF, Nicholls JT, Frost JEF, Linfield EH, Pepper M, Ford CJB, Ritchie DA, Jones GAC, Kogan E, Kaveh M: Magneticfieldinduced insulatorquantum Hallinsulator transition in a disordered twodimensional electron gas. J Phys Condens Matter 1994, 6: 4763. 10.1088/09538984/6/25/014View Article
 Laughlin RB: Levitation of ExtendedState Bands in a Strong Magnetic Field. Phys Rev Lett 1984, 52: 2304. 10.1103/PhysRevLett.52.2304View Article
 Khmelnitskii D: Quantum hall effect and additional oscillations of conductivity in weak magnetic fields. Phys Lett 1984, 106A: 182.View Article
 Liu DZ, Xie XC, Niu Q: Weak Field Phase Diagram for an Integer Quantum Hall Liquid. Phys Rev Lett 1996, 76: 975. 10.1103/PhysRevLett.76.975View Article
 Sheng DN, Weng ZY: Disappearance of Integer Quantum Hall Effect. Phys Rev Lett 1997, 78: 318. 10.1103/PhysRevLett.78.318View Article
 Sheng DN, Weng ZY: Phase diagram of the integer quantum Hall effect. Phys Rev B 2000, 62: 15363. 10.1103/PhysRevB.62.15363View Article
 Kravchenko SV, Kravchenko GV, Furneaux JE, Pudalov VM, D'Iorio M: Possible metalinsulator transition at B = 0 in two dimensions. Phys Rev B 1994, 50: 8039. 10.1103/PhysRevB.50.8039View Article
 Dobrosavljevic V, Abrahams E, Miranda E, Chakravarty S: Scaling Theory of TwoDimensional MetalInsulator Transitions. Phys Rev Lett 1997, 79: 455. 10.1103/PhysRevLett.79.455View Article
 Chang WH, Lin CH, Fu YJ, Lin TC, Lin H, Cheng SJ, Lin SD, Lee CP: Impacts of Coulomb Interactions on the magnetic response of excitonic complexes in single semiconductor nanostructures. Nanoscale Res Lett 2010, 5: 680. 10.1007/s1167101095313View Article
 Kim GH, Nicholls JT, Khondaker SI, Farrer I, Ritchie DA: Tuning the insulatorquantum Hall liquid transitions in a twodimensional electron gas using selfassembled InAs. Phys Rev B 2000, 61: 10910. 10.1103/PhysRevB.61.10910View Article
 Kim GH, Liang CT, Huang CF, Nicholls JT, Ritchie DA, Kim PS, Oh CH, Juang JR, Chang YH: From localization to Landau quantization in a twodimensional GaAs electron system containing selfassembled InAs quantum dots. Phys Rev B 2004, 69: 073311. 10.1103/PhysRevB.69.073311View Article
 Song SH, Shahar D, Tsui DC, Xie YH, Monroe D: New Universality at the Magnetic Field Driven Insulator to Integer Quantum Hall Effect Transitions. Phys Rev Lett 1997, 78: 2200. 10.1103/PhysRevLett.78.2200View Article
 Lee CH, Chang YH, Suen YW, Lin HH: Magneticfieldinduced delocalization in centerdoped GaAs/Al _{ x } Ga _{ 1x } As multiple quantum wells. Phys Rev B 1998, 58: 10629. 10.1103/PhysRevB.58.10629View Article
 Huang CF, Chang YH, Lee CH, Chuo HT, Yeh HD, Liang CT, Lin HH, Cheng HH, Hwang GJ: Insulatorquantum Hall conductor transitions at low magnetic field. Phys Rev B 2002, 65: 045303. 10.1103/PhysRevB.65.045303View Article
 Huang TY, Juang JR, Huang CF, Kim GH, Huang CP, Liang CT, Chang YH, Chen YF, Lee Y, Ritchie DA: On the lowfield insulatorquantum Hall conductor transition. Physica E 2004, 22: 240. 10.1016/j.physe.2003.11.258View Article
 Huckestein B: Quantum Hall Effect at Low Magnetic Fields. Phys Rev Lett 2000, 84: 3141. 10.1103/PhysRevLett.84.3141View Article
 Huang TY, Liang CT, Kim GH, Huang CF, Huang CP, Lin JY, Goan HS, Ritchie DA: From insulator to quantum Hall liquid at low magnetic fields. Phys Rev B 2008, 78: 113305. 10.1103/PhysRevB.78.113305View Article
 Huang TY, Huang CF, Kim GH, Huang CP, Liang CT, Ritchie DA: An Experimental Study on the Hall Insulators. Chin J Phys 2009, 47: 401.
 Huang TY, Liang CT, Kim GH, Huang CF, Huang CP, Ritchie DA: Probing twodimensional metalliclike and localization effects at low magnetic fields. Physica E 2010, 42: 1142. 10.1016/j.physe.2009.11.049View Article
 Nakamura S, Senoh M, Iwasa N, Hagahama S, Yamada Y, Mukai Y: Superbright Green InGaN SingleQuantumWellStructure LightEmitting Diodes. Jpn J Appl Phys 2 1995, 34: L1332. 10.1143/JJAP.34.L1332View Article
 Wu Y, Keller B, Keller S, Kapolnek D, Kozodoy P, DenBaars S, Mishra U: Very high breakdown voltage and large transconductance realized on GaN heterojunction field effect transistors. Appl Phys Lett 1996, 69: 1438. 10.1063/1.117607View Article
 Bulman GE, Doverspike K, Sheppard ST, Weeks TW, Kong HS, Dieringer HM, Edmond JA, Brown JD, Swindell JT, Schetzina JF: Pulsed operation lasing in a cleavedfacet InGaN/GaN MQW SCH laser grown on 6HSiC. Electron Lett 1997, 33: 1556. 10.1049/el:19971025View Article
 Mack MP, Abare A, Aizcorbe M, Kozodoy P, Keller S, Mishra UK, Coldren L, Denbaars S: Characteristics of indiumgalliumnitride multiplequantumwell blue laser diodes grown by MOCVD. MRS Internet J Nitride Semicond Res 1997, 2: 41.
 Hang DR, Liang CT, Juang JR, Huang TY, Hung WK, Chen YF, Kim GH, Lee JH, Lee JH: Electrically detected and microwavemodulated Shubnikovde Haas ocsillcations in an Al _{ 0.4 } Ga _{ 0.6 } N/GaN heterostructure. J Appl Phys 2003, 93: 2055. 10.1063/1.1539286View Article
 Juang JR, Huang TY, Chen TM, Lin MG, Lee Y, Liang CT, Hang DR, Chen YF, Chyi JI: Transport in a gated Al _{ 0.18 } Ga _{ 0.82 } N/GaN electron system. J Appl Phys 2003, 94: 3181. 10.1063/1.1594818View Article
 Cho KS, Huang TY, Huang CP, Chiu YH, Liang CT, Chen YF, Lo I: Exchangeenhanced gfactors in an Al _{ 0.25 } Ga _{ 0.75 } N/GaN twodimensional electron system. J Appl Phys 96: 7370. 10.1063/1.1815390
 Chen JH, Lin JY, Tsai JK, Park H, Kim GH, Youn D, Cho HI, Lee EJ, Lee JH, Liang CT, Chen YF: Experimental evidence for DrudeBoltzmannlike transport in a twodimensional electron gas in an AlGaN/GaN heterostructure. J Korean Phys Soc 2006, 48: 1539.
 Lin JY, Chen JH, Kim GH, Park H, Youn DH, Jeon CM, Baik JM, Lee JL, Liang CT, Chen YF: Magnetotransport measurements on an AlGaN/GaN twodimensional electron system. J Korean Phys Soc 2006, 49: 1130.
 Hang DR, Chou MMC, Hsieh MH, Heuken M: Influence of an Advanced Buffer Layer on the Optical Properties of an InGaN/GaN MQW Grown on a (111) Silicon Substrate. J Korean Phys Soc 2007, 50: 797. 10.3938/jkps.50.797View Article
 Chen KY, Liang CT, Chen NC, Chang PH, Chang CA: Weak Localization and electronelectron interaction effects in Al0.15Ga0.85N/GaN High Electron Mobility Transistor Structure. Chin J Phys 2007, 45: 616.
 Schremer AT, Smart JA, Wang Y, Ambacher O, MacDonald NC, Shealy JR: High electron mobility AlGaN/GaN heterostructure on (111) Si. Appl Phys Lett 2000, 76: 736. 10.1063/1.125878View Article
 Chen KY, Chang YH, Liang CT, Aoki N, Ochiai Y, Huang CF, Lin LH, Cheng KA, Cheng HH, Lin HH, Wu JY, Lin SD: Probing Landau quantization with the presence of insulatorquantum Hall transition in a GaAs twodimensional electron system. J Phys Condens Matter 2008, 20: 295223. 10.1088/09538984/20/29/295223View Article
 Chen KY, Liang CT, Aoki N, Ochiai Y, Cheng KA, Lin LH, Huang CF, Li YR, Tseng YS, Yang CK, Lin PT, Wu JY, Lin SD: Probing insulatorquantum Hall transitions by current heating. J Korean Phys Soc 2009, 55: 64. 10.3938/jkps.55.64View Article
 Kannan ES, Kim GHo, Lin JY, Chen JH, Chen KY, Zhang ZY, Liang CT, Lin LH, Youn DH, Kang KY, Chen NC: Experimental Evidence for Weak InsulatorQuantum Hall Transitions in GaN/AlGaN TwoDimensional Electron Systems. J Korean Phys Soc 2007, 50: 1643. 10.3938/jkps.50.1643View Article
 Li W, Csathy GA, Tsui DC, Pfeiffer LN, West KW: Direct observation of alloy scattering of twodimensional electrons in Al _{ x } Ga _{ 1x } As. Appl Phys Lett 2003, 83: 2832. 10.1063/1.1611650View Article
 Li W, Csáthy GA, Tsui DC, Pfeiffer LN, West KW: Scaling and Universality of Integer Quantum Hall PlateautoPlateau Transitions. Phys Rev Lett 2005, 94: 206807. 10.1103/PhysRevLett.94.206807View Article
 Li W, Vicente CL, Xia JS, Pan W, Tsui DC, Pfeiffer LN, West KW: Scaling in PlateautoPlateau Transition: A Direct Connection of Quantum Hall Systems with the Anderson Localization Model. Phys Rev Lett 2009, 102: 216801. 10.1103/PhysRevLett.102.216801View Article
 Shahar D, Tsui DC, Shayegan M, Shimshoni E, Sondhi SL: A Different View of the Quantum Hall PlateautoPlateau Transitions. Phys Rev Lett 1997, 79: 479. 10.1103/PhysRevLett.79.479View Article
 Minkov GM, Germanenko AV, Rut OE, Sherstobitov AA, Larionova VA, Bakarov AK, Zvonkov BN: Diffusion and ballistic contributions of the interaction correction to the conductivity of a twodimensional electron gas. Phys Rev B 2006, 74: 045314. 10.1103/PhysRevB.74.045314View Article
 Liang CT, Lin LH, Huang JZ, Zhang ZY, Sun ZH, Chen KY, Chen NC, Chang PH, Chang CA: Electronelectron interactions in Al _{ 0.15 } Ga _{ 0.85 } N/GaN high electron mobility transistor structures grown on Si substrates. Appl Phys Lett 2007, 90: 022107. 10.1063/1.2430778View Article
 Murzin SS: On the phase boundaries of the integer quantum Hall effect. Part II. JETP Lett 2010, 91: 155. 10.1134/S0021364010030112View Article
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.